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The Gauss–Legendre algorithm is an algorithm to compute the digits of π.It is notable for being rapidly convergent, with only 25 iterations producing 45 million correct digits of π.
Liu Hui's method of calculating the area of a circle. Liu Hui's π algorithm was invented by Liu Hui (fl. 3rd century), a mathematician of the state of Cao Wei.Before his time, the ratio of the circumference of a circle to its diameter was often taken experimentally as three in China, while Zhang Heng (78–139) rendered it as 3.1724 (from the proportion of the celestial circle to the diameter ...
The last 100 decimal digits of the latest world record computation are: [1] 7034341087 5351110672 0525610978 1945263024 9604509887 5683914937 4658179610 2004394122 9823988073 3622511852 Graph showing how the record precision of numerical approximations to pi measured in decimal places (depicted on a logarithmic scale), evolved in human history.
The best known approximations to π dating to before the Common Era were accurate to two decimal places; this was improved upon in Chinese mathematics in particular by the mid-first millennium, to an accuracy of seven decimal places. After this, no further progress was made until the late medieval period.
where C is the circumference of a circle, d is the diameter, and r is the radius.More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width.
The Chudnovsky algorithm is a fast method for calculating the digits of π, based on Ramanujan's π formulae.Published by the Chudnovsky brothers in 1988, [1] it was used to calculate π to a billion decimal places.
For a lattice L in Euclidean space R n with unit covolume, i.e. vol(R n /L) = 1, let λ 1 (L) denote the least length of a nonzero element of L. Then √γ n n is the maximum of λ 1 (L) over all such lattices L. 1822 to 1901 Hafner–Sarnak–McCurley constant [118]
An easy mnemonic helps memorize this fraction by writing down each of the first three odd numbers twice: 1 1 3 3 5 5, then dividing the decimal number represented by the last 3 digits by the decimal number given by the first three digits: 1 1 3 分之(fēn zhī) 3 5 5. (In Eastern Asia, fractions are read by stating the denominator first ...